An algorithm is presented which locates the global minimum or maximum of a function satisfying a lipschitz condition. The algorithm uses lower bound functions defined on a partitioned domain to generate a sequence of ...
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An algorithm is presented which locates the global minimum or maximum of a function satisfying a lipschitz condition. The algorithm uses lower bound functions defined on a partitioned domain to generate a sequence of lower bounds for the global minimum. Convergence is proved, and some numerical results are presented.
A domain partitioning algorithm for minimizing or maximizing a lipschitzcontinuous function is enhanced to yield two new, more efficient algorithms. The use of interval arithmetic in the case of rational functions an...
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A domain partitioning algorithm for minimizing or maximizing a lipschitzcontinuous function is enhanced to yield two new, more efficient algorithms. The use of interval arithmetic in the case of rational functions and the estimates of lipschitz constants valid in subsets of the domain in the case of others and the addition of local optimization have resulted in an algorithm which, in tests on standard functions, performs well.
In this paper, we introduce a new kind of Kantorovich-type Bernstein-Stancu-Schurer operators based on the concept of (p, q)-integers. We investigate statistical approximation properties and establish a local approxim...
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In this paper, we introduce a new kind of Kantorovich-type Bernstein-Stancu-Schurer operators based on the concept of (p, q)-integers. We investigate statistical approximation properties and establish a local approximation theorem, we also give a convergence theorem for the lipschitz continuous functions. Finally, we give some graphics and numerical examples to illustrate the convergence properties of operators to some functions. (C) 2015 Elsevier Inc. All rights reserved.
In this paper, we introduce a novel extension of the Bernstein-Kantorovich-Stancu type operator of degree n with the help of multiple shape parameters. Voronovskaja and Gruss-Voronovskaja type approximation theorems a...
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In this paper, we introduce a novel extension of the Bernstein-Kantorovich-Stancu type operator of degree n with the help of multiple shape parameters. Voronovskaja and Gruss-Voronovskaja type approximation theorems are examined via Ditzian-Totik moduli of smoothness. We investigate basic statistical convergence properties with respect to a non-negative regular summability matrix. Moreover, using Ditzian-Totik moduli, local and global approximation properties associated to the proposed operator have been established. Finally, several illustrative examples are presented to demonstrate the efficiency, applicability and validity of the operator. The graphical and numerical results verify that the proposed operator gives better approximation as well as expand the previous Bernstein-Kantorovich type modifications including single parameter.
This paper presents a study of the morphological slope transform in the complete lattice framework. It discusses in detail the interrelationships between the slope transform at one hand and the (Young-Fenchel) conjuga...
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This paper presents a study of the morphological slope transform in the complete lattice framework. It discusses in detail the interrelationships between the slope transform at one hand and the (Young-Fenchel) conjugate and Legendre transform, two well-known concepts from convex analysis, at the other. The operators and transforms of importance here (hull operations, slope transform, support function, polar, gauge, etc.) are complete lattice operators with interesting properties also known from theoretical morphology. For example, the slope transform and its 'inverse' form an adjunction. It is shown that the slope transform for sets (binary signals) coincides with the notion of support function, known from the theory of convex sets. Two applications are considered: the first application concerns an alternative approach to the distance transform. The second application deals with evolution equations for multiscale morphology using the theory of Hamilton-Jacobi equations. (C) 1997 Elsevier Science B.V.
Lagrange once made a claim having the consequence that a smooth function f has a local minimum at a point if all the directional derivatives of fat that point are nonnegative. That the Lagrange claim is wrong was show...
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Lagrange once made a claim having the consequence that a smooth function f has a local minimum at a point if all the directional derivatives of fat that point are nonnegative. That the Lagrange claim is wrong was shown by a counterexample given by Peano. In this note, we show that an extended claim of Lagrange is right. We show that, if all the lower directional derivatives of a locally lipschitz function f at a point are positive, then f has a strict minimum at that point.
An interval method for a class of min-max-min problems is described in this paper, in which the objective functions are lipschitzcontinuous. The convergence of algorithm is proved, numerical results from a Turbo B im...
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An interval method for a class of min-max-min problems is described in this paper, in which the objective functions are lipschitzcontinuous. The convergence of algorithm is proved, numerical results from a Turbo B implementation of the algorithm are presented. The method can get both the optimal value and all global solutions of min-max-min problem. Theoretical analysis and numerical tests indicate the algorithm is stable and reliable. (C) 2007 Elsevier Inc. All rights reserved.
In this manuscript, we propose a Polya distribution-based generalization of lambda-Bernstein operators. We establish some fundamental results for convergence as well as order of approximation of the proposed operators...
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In this manuscript, we propose a Polya distribution-based generalization of lambda-Bernstein operators. We establish some fundamental results for convergence as well as order of approximation of the proposed operators. We present theoretical result and graph to demonstrate the proposed operator's intriguing ability to interpolate at the interval's end points. In order to illustrate the convergence of proposed operators as well as the effect of changing the parameter "mu," we provide a variety of results and graphs as our paper's conclusion.
In this paper, we introduce a new kind of modified Bernstein-Schurer operators based on the concept of (p, q)-integers. We investigate statistical approximation properties, establish a local approximation theorem, giv...
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In this paper, we introduce a new kind of modified Bernstein-Schurer operators based on the concept of (p, q)-integers. We investigate statistical approximation properties, establish a local approximation theorem, give a convergence theorem for the lipschitz continuous functions, we also obtain a Voronovskaja-type asymptotic formula. Next, we construct the bivariate operators and get some convergence properties. Finally, we give some graphs to illustrate the convergence properties of operators to some functions.
The paper focuses at the estimates for the rate of convergence of the q-Bernstein polynomials (0 < q < 1) in the complex plane. In particular, a generalization of previously known results on the possibility of a...
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The paper focuses at the estimates for the rate of convergence of the q-Bernstein polynomials (0 < q < 1) in the complex plane. In particular, a generalization of previously known results on the possibility of analytic continuation of the limit function and an elaboration of the theorem by Wang and Meng is presented. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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